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Category Theory for the Sciences
Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines.
Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions.
Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
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About the Author
David I. Spivak is a Research Scientist in the Department of Mathematics at MIT.
—Piet Hut, Professor of Astrophysics and Head of the Program in Interdisciplinary Studies, Institute for Advanced Study, Princeton
—André Joyal, Fellow of the Royal Society of Canada
—John Baez, Professor of Mathematics, University of California, Riverside
—Stephen Molloy, Head of Accelerator Engineering for the European Spallation Source, and Adjunct Lecturer in Accelerator Physics, University of Lund, Sweden